Simple Groups of Finite Morley Rank with a Finitary Automorphism Group

Ulla Karhumaki (Manchester)

Frank Adams 1,

The Cherlin-Zilber Conjecture "Simple infinite groups of finite Morley rank are algebraic groups over algebraically closed fields" is considered to be one of the main open problems in the theory of omega-stable groups of finite Morley rank. Ehud Hrushovski suggested that it can be approached by proving first that a generic automorphism of a group of finite Morley rank closely resembles the behaviour of generalized Frobenius automorphisms of algebraic groups. In my recent work I take the initial step towards Hrushovskis suggestion by introducing finitary automophism groups. In my talk I prove that a simple infinite group of finite Morley rank with a finitary group of definable automorphisms is a Chevalley group over an algebraically closed field of positive characteristic.

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